We give a multivariate generalization of Borell’s noise stability theorem for Gaussian vectors. As a consequence we recover two inequalities, also due to Borell, for exit times of the Ornstein-Uhlenbeck process.

Given a probability density, we estimate the rate of decay of the measure of the level sets of its evolutes by the Ornstein-Uhlenbeck semigroup. It is faster than what follows from the preservation of mass and Markov’s inequality.

In the paper we consider problem of estimating parameters entering drift a fractional Ornstein-Uhlenbeck type process in non-ergodic case, when underlying stochastic integral is ...

We study the fluid inclusion of both Lennard-Jones (LJ) particles and particles with competing interaction ranges--short range attractive and long range repulsive (SALR)--in a disordered porous medium constructed as a controlled pore glass in two dimensions. With the aid of a full two-dimensional Ornstein-Zernike approach, complemented by a Replica Ornstein-Zernike integral equation, we explici...